There are 20 of those cards, each including 5 quests + 1 interlude + 1 finale?

?!

No, there is one included campaign consisting of 20 possible quests all but 3 of which- the inro, interlude, and finale- consist of 2 encounters. I believe 9 quests get played in one playthrough of the campaign- Intro, interlude, finale, three Act 1 quests, and three act 2 quests. This would result in 15 encounters per campaign playthrough (with the intro being a short encounter and the interlude and finale being much longer encounters).

There's 20 quests, although not all of them are intended to be run as one-shots (both interlude and both finale quests are intended only as part of the campaign, according to the instructions, although personally I don't see any reason they can't be run as a one-shot quest). Of those quests, 3 of them - the initial quest "First Blood" and the two interlude quests - have only one encounter. The rest are all spread across two encounters, with success in the first encounter determining possible benefits for one or both sides in the second.

As for how the campaign works, it always flows as the intro, 3 act 1 quests, interlude, 3 act 2 quests, and finale. After the intro, whoever won the quest picks one of the act 1 quests, it's played and marked off on the campaign sheet who won, and the winner picks the next quest. This goes on until three quests are finished, and the game goes to the Interlude. If the heroes won at least two act 1 quests, they go to Interlude 1, if the overlord won at least two, they go to Interlude 2.

After that, the overlord upgrades all his monsters and lieutenants to act 2 stats, the heroes are allowed to buy stuff from the act 2 item deck, and the game continues with three more quests from act 2, with the winner of the last quest picking which one to do next. There's 10 quests in act 2, with each act 1 quest linking to two act 2 quests. For each pair of quests, the only one available depends on if the heroes or overlord won the associated act 1 quest (or, if the quest was never attempted, it's assumed the overlord won it).

For example, look at the campaign sheet linked earlier. If the heroes played and won the quest A Fat Goblin, then The Master's Hoard is available and The Frozen Spire is locked out permanently. If the overlord won (or if A Fat Goblin wasn't attempted at all), then The Master's Hoard is locked out and The Frozen Spire is available.

Again, after three act 2 quests are finished, which side won at least two of them determines which finale to go to - Finale 1 if the heroes won more, or Finale 2 if the overlord won more. Whoever wins the finale quest wins the entire campaign, with progress up to that point determining how powerful each respective side is.